function w = GetaT_vec(invP,j,v)
    
    k = 1/invP.disT(1,2);

    tmp = zeros(invP.mesh.nf,1);
    for ii = 1:invP.nt
        for jj = 1:invP.ntx
            if ii == 1
                tmp = tmp + sdiag(j{ii}(:,jj))*v{ii}(:,jj);
            else
                tmp = tmp + sdiag( j{ii}(:,jj) - j{ii-1}(:,jj) )*v{ii}(:,jj);
            end
        end
    end
    w = sdiag(k*invP.tauModel)*invP.mesh.Af'*tmp;